A note on conformal vector fields on a Riemannian manifold

2014 ◽  
Vol 136 (1) ◽  
pp. 65-73 ◽  
Author(s):  
Sharief Deshmukh ◽  
Falleh Al-Solamy
Keyword(s):  
Riemannian Manifold ◽  
Vector Fields ◽  
Conformal Vector ◽  
Conformal Vector Fields

scholarly journals A classification of conformal vector fields on the tangent bundle

2020 ◽  
Vol 72 (5) ◽  
Author(s):  
Zohre Raei ◽  
Dariush Latifi
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Conformal Transformations ◽  
Conformal Vector ◽  
Conformal Vector Fields

UDC 514.7 Let ( M , g ) be a Riemannian manifold and T M be its tangent bundle equipped with a Riemannian (or pseudo-Riemannian) lift metric derived from g .  We give a classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle.

scholarly journals Closed conformal vector fields on pseudo-Riemannian manifolds

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
D. A. Catalano
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Geometric Proof ◽  
Conformal Vector Field ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Local Coordinates

We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.

scholarly journals Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 863
Author(s):  
Amira Ishan ◽  
Sharief Deshmukh ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Differential Equation ◽  
Riemannian Manifold ◽  
Vector Field ◽  
Nontrivial Solution ◽  
Vector Fields ◽  
Dimensional Sphere ◽  
Conformal Vector Field ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
De Rham

We study the effect of a nontrivial conformal vector field on the geometry of compact Riemannian spaces. We find two new characterizations of the m-dimensional sphere Sm(c) of constant curvature c. The first characterization uses the well known de-Rham Laplace operator, while the second uses a nontrivial solution of the famous Fischer–Marsden differential equation.

Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri ◽  
Cornelia-Livia Bejan
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Conformal Vector ◽  
Conformal Vector Fields

SINGULAR FOLIATION GENERATED BY AN ORBIT OF FAMILY OF VECTOR FIELDS

2021 ◽  
Vol 10 (4) ◽  
pp. 2141-2147
Author(s):  
X.F. Sharipov ◽  
B. Boymatov ◽  
N. Abriyev
Keyword(s):  
Dynamical Systems ◽  
Euclidean Space ◽  
Control Theory ◽  
Vector Fields ◽  
Singular Foliation ◽  
Completely Integrable ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Systems Control

Geometry of orbit is a subject of many investigations because it has important role in many branches of mathematics such as dynamical systems, control theory. In this paper it is studied geometry of orbits of conformal vector fields. It is shown that orbits of conformal vector fields are integral submanifolds of completely integrable distributions. Also for Euclidean space it is proven that if all orbits have the same dimension they are closed subsets.

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